Solve the system by triangularizing the augmented matrix and using back substitution. If the system is linearly dependent, give the solution in terms of a parameter.
A) (1, -3, 2)
B) (1, -3, 1)
C) coincident dependence; {(x, y, z) | 2x + y - 3z = -7}
D) no solution, inconsistent

Question

Solve the system by triangularizing the augmented matrix and using back substitution. If the system is linearly dependent, give the solution in terms of a parameter. 
A) (1, -3, 2) 
B) (1, -3, 1) 
C) coincident dependence; {(x, y, z) | 2x + y - 3z = -7} 
D) no solution, inconsistent

Quizplus · Accepted Answer

Triangularizing the augmented matrix gives:
\begin{bmatrix}2 & 1 & -3 & -7\0 & -1 & 5 & 17\0 & 0 & 0 & 0\end{bmatrix}
This system has two nonzero rows, and the leading entry of the second row is not a multiple of the leading entry of the first row. Therefore, the system has a unique solution. Using back substitution, we find that z = t, y = 5t + 17, and x = -y/2 - (3/2)z - 7/2. Thus, the general solution is {(x, y, z) | x = -5t/2 - 3z/2 - 7/2, y = 5t + 17, z = t}.

Solve the System by Triangularizing the Augmented Matrix and Using